Scattering of Magnetoacoustic Waves and Dynamic Stress Concentration around Double Openings in Piezomagnetic Composites

Based on the magnetoacoustic coupled dynamics theory, the wave function expansion method is used to solve the problem of acoustic wave scattering and dynamic stress concentration around the two openings in e-type piezomagnetic composites. To deal with the multiple scattering between openings, the local coordinate method is introduced. The general analytical solution to the problem and the expression of the dynamic stress concentration are derived. As an example, the numerical results of the dynamic stress distribution around two openings with equal diameters are given. The effects of the parameters, such as the incident wave number and the spacing between the openings, on the dynamic stress concentration factor are analyzed.

Dynamic Stress Analysis of a Circular-Lined Tunnel in Composite Strata-SH Wave Incidence

It is necessary to study the problem of seismic wave scattering in composite stratum for tunnel engineering because the existence of composite strata will make the stress of tunnels more complicated during earthquakes. In this thesis, a series solution of the scattering wave field of the composite strata and lining is obtained using the complex function method. According to the stress and displacement boundary conditions between the composite stratum and the lining, a series of equations are established and are solved by means of Fourier transformation and finite term truncation, and the calculation errors are also discussed. Through programming calculations, the dynamic stress concentration factor (DSCF) of circular tunnels in the two types of composite strata, “hard-over-soft” and “soft-over-hard,” is analyzed when SH waves propagate, and certain conclusions on the scattering of SH waves that are distinguished from the case of single homogeneous layers are reached. The research in this article reveals some phenomena. For the Q345 steel lining in the calculation examples, it is found in this paper that increasing the thickness of the lining is effective to reduce the influence of the DSCF. But, for C30 concrete, increasing the thickness of the lining reduces the DSCF of the outer surface while increasing the DSCF of the inner surface.

Scattering of Incident P-Waves by a Semicylindrical Core-Shell Structure in an Elastically Constrained Half-Space at Nanoscale

Under the premise of the theory of surface elasticity, the scattering of plane compressional waves (P-waves) in the surface of a semicylindrical core-shell structure within the nanoscale elastic confinement half-space is studied by using the method of eigen-function expansion. The generalized Y-L equation is used to give the nanoscale boundary conditions, and the dynamic stress concentration factor (DSCF) along the interface of core-shell structure induced by the plane elastic wave are derived and numerically evaluated. Under different incident wave frequencies, surface energy, and shear modulus, when the radius of the core-shell structure is reduced to the nanometer level, their influence on the DSCF is very significant. These have been confirmed by numerical calculations.

Scattering of SH Wave by a Semi-Circle Inclusion Embedded in Bi-Material Half Space Surface

ABSTRACTInvestigation of SH wave scattering by inclusions in bi-material half space is an important issue in engineering. The purpose of this work is to study the dynamic response of a semi-circle inclusion embedded in bi-material half space surface by SH wave. Graf's addition theorem, Green function method and region-matching technique are used to determine the displacement fields in the bi-material half space and the inclusion. The distributions of dynamic stress concentration factor (DSCF) around the semi-circle inclusion are depicted graphically considering different material parameters. The results show that the frequency and the incidence angle of SH wave, the rigidities of the inclusion and bi-material half space, and the distance from the inclusion to the interface have a great effect on the distribution of DSCF around the inclusion.

Dynamic Stress around a Cylindrical Nano-Inclusion with an Interface in a Right-Angle Plane under SH-Wave

Based on the surface elasticity theory, the scattering of shear wave (SH-wave) by a cylindrical nano-inclusion with an interface in a right-angle plane is studied using the method of complex variable function. The dynamic stress concentration factor along the interface of inclusion by the SH-wave and scattering cross section are derived and numerically evaluated. The surface effect, the incident wave’s frequency, the shear modulus, and the distances from the center of nano-inclusion to the right-angle boundaries show the different degrees effects on the DSCF. Our results can aid in analyzing the mechanical properties of nonuniform nanocomposites. The proposed method can better solve the scattering problem of the holes/inclusions on noninfinite elastic substrates.

Scattering of SH-Wave by a Circular Inclusion Near the Interfacial Cracks in the Piezoelectric Bi-Material Half-Space

With the aid of the Green's function method and complex function method, the scattering problem of SH-wave by a circular inclusion near the two symmetrically permeable interfacial cracks in the piezoelectric bi-material half -space is considered to obtain the steady state response. Firstly, by means of the image method, the essential function of Green's function is constructed, which satisfies the stress free and electric insulation conditions on the horizontal boundaries in a right-angle space including a circular inclusion and bearing a harmonic out-plane line source force on the vertical boundary. Secondly, the bi-material media is divided into two parts along the vertical boundary. According to continuity condition, the first kind of Fredholm integral equations containing undetermined anti-plane forces are established by “the conjunction method” and “the crack-division technology”, then the integral equations are reduced to the algebraic equations including finite items by effective truncation. Finally, the dynamic stress concentration factor around the edge of circular inclusion and dynamic stress intensity factor at the crack tip are calculated, then the influences of the frequency of incident wave, the length of crack, the position of the crack, the position of circular inclusion, etc. on the dynamic stress concentration factor and dynamic stress intensity factor are discussed.

Scattering of SH Wave by a Cylindrical Inclusion and a Semi-Cylindrical Hollow Near Vertical Interface Crack in the Bi-Material Half Space

With the aid of the Green's function method and complex function method, the scattering problem of SH-wave by a cylindrical inclusion and a semi-cylindrical hollow in the bi-material half space is considered to obtain the steady state response. Firstly, by the means of the image method, the essential solution of displacement field as well as Green's function is constructed which satisfies the stress free on the horizontal boundary in a right-angle space including a cylindrical inclusion and a semi-cylindrical hollow and bearing a harmonic out-plane line source force at any point on the vertical boundary. Secondly, the bi-material half space is divided into two parts along the vertical interface, and the first kind of Fredholm integral equations containing undetermined anti-plane forces at the linking section is established by “the conjunction method” and “the crack-division method”, the integral equations are reduced to the algebraic equations consisting of finite items by effective truncation. Finally, dynamic stress concentration factor around the edge of cylindrical inclusion and dynamic stress intensity factor at crack tip are calculated, and the influences of effect of interface and different combination of material parameters, etc. on dynamic stress concentration factor and dynamic stress intensity factor are discussed.

Dynamic Response of Multiple Holes in Half Space Saturated Soil to the Effect of the P Waves

According to the Biot wave theory and the complex function combined with multi coordinate method, seismic wave dynamic response of underground holes in the half space saturated soil is studied. Given P wave on two circular holes of the dynamic stress concentration factor of the numerical results, the distribution situations of the dynamic stress concentration factors are discussed with the variation of the hole spacing, incidence angle and the dimensionless wave number. The results show that, the effect of the underground hole spacing to the interaction effects of the holes is obvious. When the hole spacing reaches up to 6 times the radius of the hole, the peak value of the dynamic stress concentration factor decreases obviously, and the peripheral distribution of offset is weakened. With increasing of the incident angle, the hole peripheral stress concentration coefficient showed the trend of first increasing then decreasing, distribution also occurs at certain angle deflection. In low frequency waves, the hole stress peak value will influence mutually more, while in the high frequency input, interaction between holes will reduce.